I think this cat is hanging around on a curtain or drapes rail. Im always amazed at a cat's ability to be able to climb to and stay in some really awkward positions. I could never understand though why cats sometimes get stuck in trees.
I think they are fighting. You can see how the sparrow is struggling. But its a mighty effort to go head to head with the pigeon. Note how the other pigeon is just standing by - perhaps he is the referee. Id like to think they could come to some arrangement to share the food.